# A pizza place offers 3 different cheeses and 8 different toppings. In how many ways can a pizza be made with 1 cheese and 3 toppings?

##### 1 Answer

We assume the three toppings must be different.

#### Explanation:

**Cheese** :

**Toppings** : **IF** the order of toppings were important -- which it isn't. This number is called the number of **permutations** .

Three things can be ordered in 6 ways (try this), so in the 336 permutations, there are groups of 6 that amount to the same **combination** :

123=132=213=231=312=321, etc.

So we have to divide the number of permutations by the number of orders to reach the number of combinations:

There are thus 336 : 6 = 56 possibilities for the toppings.

Since we need cheese AND toppings we multiply:

Number of different pizzas: 3 x 56 = 168.

**Calculator** : if you have the nCr function the answer would be:

3 x 8 nCr 3 = 168